Evaluate the function requested. Write your answer as a fraction in lowest terms.
Triangle A B C. Angle C is 90 degrees. Hypotenuse A B is 25, Adjacent A C is 15, Opposite C B is 20.
Find sin A.
a.
sine A = four-fifths
c.
sine A = three-fifths
b.
sine A = four-thirds
d.
sine A = five-fourths
see picture.......

Answer:

  20 feet

Step-by-step explanation:

You want the distance between the zeros of the function y = -11/50(x -4)(x -24), where x and y are in feet.

The function value is zero when the factors are zero:

  x -4 = 0   ⇒   x = 4

  x -24 = 0   ⇒   x = 24

The distance between these values on the x-axis is ...

  24 -4 = 20

The width of the tunnel at ground level is 20 feet.

The given expression at a = 9 and b = 8 is equivalent to 71.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the mathematical expression as -

{b + 7a}

Given is the expression as -

{b + 7a}

For a = 9 and b = 8, we can write -

{b + 7a}

{8 + 7 x 9}

{8 + 63}

71

Therefore, the given expression at a = 9 and b = 8 is equivalent to 71.

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{The complete question is -

evaluate the expression when a = 9 and b = 8 :

b + 7a}

The 3/2cm unit rate corresponds to the proportional relationship shown in the graph.

What is the rate of change?

The term "rate of change" (ROC) describes the rate at which something changes over time. Thus, it is not the number of individual changes themselves but rather the acceleration or deceleration of changes (i.e., the rate). The rate of change is a tool used in finance to comprehend price returns and spot trend momentum.

Here, we have

Given: points (0, 0) and (6, 9)

The term for the rate of change is the slope.  

This means to find the unit rate, we use the formula for slope:

m = (y₂-y₁)/(x₂-x₁)

m = (9-0)/(6-0)

m = 9/6

m = 3/2cm

Hence, the 3/2cm unit rate corresponds to the proportional relationship shown in the graph.

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Answer:  120

120 x 0.85 = 102

Have a good day!

Answer: 120

Step-by-step explanation: (102 x 100) / 85

The inverse equations are F(x)⁻¹ = 2x - 20 and F(x)⁻¹ = ( x/ 8) + ( 3 /8).

A function is defined as the expression that set up the relationship between the dependent variable and the independent variable. In an inverse function, the value of two variables x  and y are interchanged,  and then the value of y is given an inverse function.

Given that the two equations are y= 1/2X+10 and y= -8X+3. The value of  inverse functions will be calculated by replacing the x and y values and solving for y,

y = 1/2X+10

x = y / 2 + 10

y = 2x - 20

The inverse of the second equation is calculated as,

y= -8x+3

x = -8y + 3

y = x / 8 + 3 / 8

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Answer:

No solutions.

1.5 is not an integer.

We know that the integers are the numbers that include positive whole numbers, negative whole numbers, and zero.

The set of integers is denoted by I

From above definition of integers, I = W(-) ∪ {0} ∪ W(+)

where W is the set of whole numbers

The set of whole numbers W =  {0, 1, 2, 3, . . ., ∞}

and the set of integers I = {. . ., -3, -2, -1, 0, 1, 2, 3, . . .}

A set of integers do not include fractions or decimals.

here we have been given a number 1.5 which is a decimal number.

By definition of integers, a number 1.5 can not be an integer.

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Answer:

A. Let x be the number of hours for which the companies charge the same amount.

Party Time: 100 + 50x = 175 + 25x

Let's Dance Company: 175 + 25x = 100 + 50x

B. To solve this system of equations, we can use substitution. We can start by isolating one of the variables on one side of the equation and then substitute that expression into the other equation.

x = 25

C. To show that the solution results in the same charge for both companies, we can substitute the value of x back into the equations for each company and see if they are equal.

Party Time: 100 + 50(25) = 100 + 1250 = 1350

Let's Dance Company: 175 + 25(25) = 175 + 625 = 800

1350 = 800

The two companies charge the same amount for 25 hours.

If the half-life of nitrogen is 10 minutes, the gram that will be left out of 120 grams of nitrogen after 120minutes is 30grams

Half-life, in radioactivity is the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay (change spontaneously into other nuclear species by emitting particles and energy), or, equivalently, the time interval required for the number of disintegrations per second of a radioactive.

The half life is expressed as:

half life = 0.693/decay constant

The half life of Nitrogen is 10minutes

therefore 10 minutes = 1/2 of 120grams

20minutes = 1/4 of 120 = 120/4 = 30 grams.

Therefore the mass of nitrogen atom that will left in 20minutes is 30grams

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Answer:

x=1 and y= -2

Step-by-step explanation:

4x-3y=10------------------------->eqn1

3x+5y=-7------------------------->eqn2

to eliminate, (eqn1 X 3) and (eqn2 X -4)

12x-9y=30------------------>eqn3

-12x-20y=28--------------->eqn4

eliminate the variable x (12x-12x)

Now,

-9y-20y=30+28

-29y=58

y=58/-29

 = -2

from eqn1,

4x-(-2 X 3)= 10

4x+6= 10

4x=10-6

    =4

x=4/4

 =1

A simplified expression for the perimeter of the triangle would be = 2(2x +7)

The perimeter of a triangle is defined as the summation of the total sides of the triangle which is made up of three sides.

The length of the base of the triangle = X

The length of first side = 11 +2x

The length of the second side= 3 + X

The perimeter = X + 11 +2x + 3 + X

= 2x + 2x + 14

= 4x + 14

= 2(2x +7)

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Yes, there are formulas in algebra. Algebra is a branch of mathematics that deals with mathematical equations and their properties. Some common formulas in algebra include the quadratic formula, the slope-intercept form of a linear equation, and the distance formula. These formulas can be used to solve a wide variety of mathematical problems involving equations and variables.

1.  (a + b)^2 = a^2 + 2ab + b^2

2.  (a - b)^2  = a^2 - 2ab + b^2

3.  (a + b) (a - b)  = a^2 - b2

4.  (x + a)(x + b)  = x^2 + (a + b)x + ab

5.  (x + a)(x - b)  = x^2 + (a - b)x - ab

6.  (x - a)(x + b)  = x^2 + (b - a)x - ab

7.  (a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)

8. a^3 + b^3 + c^3 - 3abc = (a + b + c ) ( a^2 + b^2 + c^2 – ab – bc – ca ) + 3abc

9. a^3 + b^3 + c^3 = 3abc   (if a + b + c = 0)

An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

With the use of mathematical expressions, algebra is the area of mathematics that helps to depict situations or problems.

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The volume of 3-dimensional shape is 5 cubic feet.

A cuboid is a solid in three dimensions with six rectangular faces, eight vertices, and twelve edges. Three dimensions, including length, breadth, and height, define a cuboid. A cuboid with integer edges is referred described as being perfect.

Given:

3-D shape is a cuboid.

The volume of the cuboid,

= length x width x height.

Substituting the values,

The volume of the cuboid,

= 5/2 x 3/2 x 4/3.

= 60/12

= 5 cubic feet.

Therefore, the volume is 5 cubic feet.

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The amount owed in 20 years is $712.08.

Compound interest simply refers to the fact that an investment, loan, or bank account's interest accrues exponentially over time as opposed to linearly over time. The word "compound" is crucial here.

Compound interest is when you receive interest on both your interest income and your savings.

Given:

P= $325

R= 4%

n= total years = 20 year

So, A = P [tex](1+ r)^n[/tex]

A = 325 [tex](1+ 4/100)^{20[/tex]

A = 325  [tex](1+ 0.04)^{20[/tex]

A = 325 x 2.191

A = 712.08

Hence, the amount is $712.08

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To find the number that makes the ratio 8:9 equivalent, we need to first understand the concept of equivalent ratios.Therefore, 9 is the number that makes the ratio 8:9 equivalent.

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Answer: 5$ took test

Step-by-step explanation:

Answer:

Step-by-step explanation:

5 is the answer

Answer:in 6 hours, she will make 30

Step-by-step explanation:

12min = 1 ring..

1min =1/12 ring..

6×60min = 1/12×360ring

=30 rings

Answer:

30

Step-by-step explanation:

12x5=60=1 hour

She can make 5 rings in one hour

5x6=30

Therefore she can make 30 in 6 hours

Answer: $2,704.00

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 2,500.00(1 + 0.04/1)(1)(2)

A = 2,500.00(1 + 0.04)(2)

A = $2,704.00

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $2,500.00 at a rate of 4% per year compounded 1 times per year over 2 years is $2,704.00.

Observations are the collection of measurements made for a specific element. Observations are typically collected from a sample of data, which are then used to measure particular variables. This information is then used to make inferences about a larger population, often referred to as a census.

A set of measurements collected for a particular element is called observations. Observations are typically generated from a sample of data which is then used to measure particular variables. Variables are measurable characteristics which can be observed and measured. For example, a variable can be a person’s age, height, or gender. The data collected from these variables are then used to make inferences about a larger population, such as a census. A census is a complete count of a population, which may be used to measure the characteristics of a population or to make estimates about a population. Observation data is used to make inferences about a larger population and is used to make decisions or draw conclusions about a particular element. This data is often used in research, policy making, and decision-making.

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Answer:

C 40m + 0.73

Step-by-step explanation:

since it is 40 per month it would be 40m because the m stands for how many months the chocolate factory charges for delivery and the extra .73 for every chocolate bar is an add on which would make this 40m + 0.73

The lettered measurements for angles or sides in descending order is a, b, c.

When a pattern of numbers in mathematics has a decreasing value, the numbers are said to be in descending order. It indicates that the numbers are sorted from highest to lowest.

A format where items are arranged from highest to lowest is known as descending order. These ideas have to do with money, fractions, decimals, and numbers.

In right triangle, the sides facing the acute angles are opposite to the angles. From the given triangle, you can see that:

Side "b" is facing angle 50°

Side "c" is the smallest side which facing the unknown angle (40°)

the third side is largest side of right triangle facing the angle 90°. this is the smallest side of second triangle because of side opposite to smallest angle.

Side "a" is facing the unknown angle of second triangle (100°)

So the correct descending order is a, b, c.

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The distance between two opposite corners of the prism is 13.

The distance between two opposite corners of a rectangular prism can be found using the Pythagorean theorem, which states that the square of the distance between two points is equal to the sum of the squares of the distances along the two axes that are perpendicular to each other.

In this case, the two opposite corners of the prism are the top-front corner and the bottom-back corner. The distance between these two corners is the hypotenuse of a right triangle with legs of length 3 (the length of the prism), 4 (the width of the prism), and 12 (the height of the prism).

So, using the Pythagorean theorem (a² + b² = c²), the distance between two opposite corners of the top of the rectangular prism is (3² + 4² = 5²) 5.

To determine the distance between two opposite corners of the prism, get the diagonal distance of the cross section made by the two opposite corners of the top of the rectangular prism.

d² = 5² + 12²

d = 13

Hence, the distance between two opposite corners of the prism is 13.

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The required solutions to the given equation are x = 0, x = -3 +√41, and x = -3-√41.

The quadratic equation is defined as a function containing the highest power of a variable is two.

The equation is given in the question, as follows:

4x⁽⁴⁾ + 24x⁽³⁾- 128x⁽²⁾ = 0

Factor out 4x² from the equation,

4x²(x² + 6x - 32) = 0

Using the zero factor principle, then

4x² = 0 and (x² + 6x - 32) = 0

After solving the above quadratic equation, we get the values:

x = 0, x = -3 +√41, and x = -3-√41

Thus, the required solutions are x = 0, x = -3 +√41, and x = -3-√41.

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Gerald read  ( 4 / 7 ) more of the book comparing to book read by Mary.

As given in the question,

Portion of book read by Gerald is equal to ( 6 / 7 ).

Portion of book read by Mary is equal to ( 2 / 7 ).

( 6 / 7 ) is greater than  ( 2 / 7 )

Gerald read more portion of the book comparing to Mary.

Difference between the portion read by Gerald and Mary is given by :

= ( 6 / 7 ) - ( 2 / 7 )

Both are like fractions Least common multiple is 7.

= ( 6 - 2 ) / 7

=  ( 4 / 7 )

Therefore, the Gerald read ( 4 / 7 ) more portion of the same book than Mary read.

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The Initial value is computed at: 190

The Growth Factor is computed at: 0.5

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth. When the input variable x appears as an exponent in the formula f(x) = axe, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x.

Given: Q = 190 / 2t

To compute: If [tex]Q = ab^t}[/tex]

Then,

→ 1 / aˣ = (1 / a)ˣ

Now we know that:

∵ (1 / aˣ) = (1 / a)ˣ

⇒ Q = 190 / 2t = 190 * (1 / 2t)

⇒ Q = 190 * (1 / 2)

[tex]Q = 190 * (\frac{1}{2})^{t}[/tex]

[tex]Q = 190 * (0.5)^{t}[/tex]

Comparing the aforementioned expression to:

[tex]Q = ab^{t}[/tex]

Initial Value, a = 190

Growth Factor, b = 0.5

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Using properties of quadrilaterals, the value of z = 48.

A quadrilateral has four straight sides and is a two-dimensional shape.. Quadrilaterals encompass geometries of parallelograms, trapezoids, rectangles, kites, squares, and rhombuses. What four characteristics does a quadrilateral have? There are four of them. There are four of them. 360° is the total of all interior angles. There are two diagonals in them.

The supplied figure makes it obvious that x=90 degrees because it is right-angled.

The figure is a kite, thus 5y+2=42, 5y=40, and y=8 are the results.

Since it's a kite, angle B must equal angle D, thus if we take ADO produces a triangle with O as the midpoint, thus x+z+42=180, 90+42+z=180, z=180-132, z=48.

This is the concrete answer.

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Yes, the given equations are consistent. Both of the equations are linear equations with the same slope and can be written in the standard form of ax + by = c. Since both of the equations have the same values of a, b, and c, they are consistent and have a single solution.

The equations can be solved by elimination, substitution, or graphing. To solve by elimination, multiply the first equation by two and subtract it from the second equation. This yields the equation

0 + 3y - 18 = 0, which can be simplified to

3y = 18. Then, substitute

3y = 18 into the first equation to solve for x. The solution is

(x, y) = (6, 6).

The given equations are

2x+3y−9=0 and

4x+6y−18=0.

These equations are both linear equations that can be written in the standard form of ax + by = c. Since the values for a, b, and c are the same in both equations, they are consistent and have a single solution. The equations can be solved by elimination, substitution, or graphing. To solve by elimination, multiply the first equation by two and subtract it from the second equation. This yields the equation 0 + 3y - 18 = 0, which can be simplified to 3y = 18. Then, substitute 3y = 18 into the first equation to solve for x. The solution is (x, y) = (6, 6). This is the only solution to the given equations, thus proving that the equations are consistent.

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The complete question is

Which of the following is correct for given equations 2x+3y−9=0 and 4x+6y−18=0 consistent and dependent.

Answer:

sheep and goats fed with silphuim were said to produce more succulent meal

An inequality can be written in two different ways depending on the desired result. In both cases, the inequality is used to represent the desired result of Mario earning no more than or more than $500.

If Mario wants to earn no more than $500:

I ≤ 500

If Mario wants to earn more than $500:

I > 500

An inequality can be written in two different ways depending on the desired result. In the first case, Mario wants to earn no more than $500. This can be written as I ≤ 500, which means "I is less than or equal to 500". The symbol ≤ indicates that the maximum value for I is 500. In the second case, Mario wants to earn more than $500. This can be written as I > 500, which means "I is greater than 500". The symbol > indicates that the minimum value for I is 500. In both cases, the inequality is used to represent the desired result of Mario earning no more than or more than $500.

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[tex]\qquad \qquad \textit{binomial theorem expansion} \\\\ \qquad \qquad (3-5z)^{14}~\hspace{4em} \begin{array}{clcl} term&coefficient&value\\ \cline{1-3}&\\ 1&+1&(3)^{14 }(-5z)^0\\ 2&+14&(3)^{13}(-5z)^1\\ 3&+91&(3)^{12}(-5z)^2\\ 4&+364&(3)^{11}(-5z)^3\\ 5&+1001&(3)^{10}(-5z)^4 \end{array} \\\\[-0.35em] ~\dotfill\\\\ 3^{14}-14(3^{13})(5z)+91(3^{12})(5z)^2-364(3^{11})(5z)^3+1001(3^{10})(5z)^4 \\\\\\ 4782969-111602610z+1209028275z^2-8060188500z^3+13299311025z^4[/tex]

I find the key to binomial expansion is mainly to get coefficient that goes next as  you see in the middle of the table above.

now, if wonder how I get it sequentially, namely as I go, for example, how did I get 91?  

well, (14 * 13 )/ 2

the current coeffient times the exponent of the 1st term divided by the "exponent of the 2nd term plus 1"

how did I get 1001?

well, (364 * 11) / 4

and so on.